From db06300320d1bebd9a231a3908ca8bb0682761f2 Mon Sep 17 00:00:00 2001
From: Chris Wells <chris@mathematicaster.org>
Date: Tue, 29 Sep 2026 09:40:15 -0400
Subject: Updated paper abstract + updated flake inputs

---
 data/papers.bib |  2 +-
 flake.lock      | 32 ++++++++++++++++----------------
 flake.nix       |  2 +-
 3 files changed, 18 insertions(+), 18 deletions(-)

diff --git a/data/papers.bib b/data/papers.bib
index fb9ae90..f9bde4b 100644
--- a/data/papers.bib
+++ b/data/papers.bib
@@ -19,7 +19,7 @@
   eprintclass = {math.CO},
   archivePrefix = {arXiv},
   archiveClass = {math.CO},
-  abstract = {We study a finite form of the classical interval discrepancy problem. Starting from the unit interval, one repeatedly splits an existing interval into two until $n$ intervals have been produced. The discrepancy of such a process is the maximum, over all intermediate stages, of the ratio between the longest interval and the shortest interval. A theorem of de Bruijn and Erdős from 1949 shows that this ratio must approach $2$ as $n\to\infty$, and they give a sharp construction achieving this bound. For fixed $n$, their construction gives the upper bound $\operatorname{disc}(n)\leq 2-\frac{3}{2n}+O(1/n^2)$. In this paper, we improve the first-order term of this bound. Specifically, we construct a strategy, called <em>lex-merge</em>, with $\operatorname{disc}(n)\leq 2-\frac{4\ln 2}{n}+O(1/n^2)$. We prove also the lower bound $\operatorname{disc}(n)\geq 2-\frac{6\ln 2}{n}-O(1/n^2)$, showing that the first-order term in this improvement over the de Bruijn&ndash;Erdős construction has the correct order of magnitude. We conjecture that the lex-merge strategy is optimal for every $n$.},
+  abstract = {We study a finite form of the classical interval discrepancy problem. Starting from the unit interval, one repeatedly splits an existing interval into two until $n$ intervals have been produced. The discrepancy of such a process is the maximum, over all intermediate stages, of the ratio between the longest interval and the shortest interval. A theorem of de Bruijn and Erdős from 1949 shows that this ratio must approach $2$ as $n\to\infty$, and they give a sharp construction achieving this bound. For fixed $n$, their construction gives the upper bound $\operatorname{disc}(n)\leq 2-\frac{3}{2n}+O\bigl({1\over n^2}\bigr)$. In this paper, we prove that $\operatorname{disc}(n)=2^{1-1/\lceil n/2\rceil}=2-{4\ln 2\over n}+O\bigl({1\over n^2}\bigr)$ for every $n$.}
 }
 
 @article{briggs_gromov,
diff --git a/flake.lock b/flake.lock
index 89bb26b..904e281 100644
--- a/flake.lock
+++ b/flake.lock
@@ -5,11 +5,11 @@
         "nixpkgs-lib": "nixpkgs-lib"
       },
       "locked": {
-        "lastModified": 1778716662,
-        "narHash": "sha256-m1Yf0wZ8j1OHjTc2UwHwyQRSnNeSgLJOd7q5Y45hzi4=",
+        "lastModified": 1788450739,
+        "narHash": "sha256-glZLQlzIn1fXH6PazR2iUmTo7kzzyYSshrWhLS9TqCU=",
         "owner": "hercules-ci",
         "repo": "flake-parts",
-        "rev": "f7c1a2d347e4c52d5fb8d10cb4d94b5884e546fb",
+        "rev": "31729ca8cbdb4fa927b34e5f4353e6a83f39e993",
         "type": "github"
       },
       "original": {
@@ -35,11 +35,11 @@
     },
     "nix-filter_2": {
       "locked": {
-        "lastModified": 1730207686,
-        "narHash": "sha256-SCHiL+1f7q9TAnxpasriP6fMarWE5H43t25F5/9e28I=",
+        "lastModified": 1757882181,
+        "narHash": "sha256-+cCxYIh2UNalTz364p+QYmWHs0P+6wDhiWR4jDIKQIU=",
         "owner": "numtide",
         "repo": "nix-filter",
-        "rev": "776e68c1d014c3adde193a18db9d738458cd2ba4",
+        "rev": "59c44d1909c72441144b93cf0f054be7fe764de5",
         "type": "github"
       },
       "original": {
@@ -50,11 +50,11 @@
     },
     "nixpkgs": {
       "locked": {
-        "lastModified": 1782911522,
-        "narHash": "sha256-ucCmt+bn4JGfGitaFgiQMHPfODqMIZ9nbHKDVHIRL7w=",
+        "lastModified": 1790687781,
+        "narHash": "sha256-/pNu7+ay1nb87v6FlT5jFQlw6Wfov3k78qll4ajPUmc=",
         "owner": "nixos",
         "repo": "nixpkgs",
-        "rev": "a1a6f0fe5442349fc15b6eb956b25d4b2fc21619",
+        "rev": "99358e9409a4d8ed0a08328b22316a3681814906",
         "type": "github"
       },
       "original": {
@@ -65,11 +65,11 @@
     },
     "nixpkgs-lib": {
       "locked": {
-        "lastModified": 1777168982,
-        "narHash": "sha256-GOkGPcboWE9BmGCRMLX3worL4EMnsnG8MyKmXNeYuhQ=",
+        "lastModified": 1788057806,
+        "narHash": "sha256-DTQSMxzDWmT0zhguthvegnVkn7CFqGCv4IHCzk5ZUpM=",
         "owner": "nix-community",
         "repo": "nixpkgs.lib",
-        "rev": "f5901329dade4a6ea039af1433fb087bd9c1fe14",
+        "rev": "596e2e3940e09b2abbeb03f75fa1828c57fcd72c",
         "type": "github"
       },
       "original": {
@@ -129,11 +129,11 @@
         "systems": "systems_2"
       },
       "locked": {
-        "lastModified": 1770582573,
-        "narHash": "sha256-dmFQ5Wis0XZznnvARSX7kHt+GFl7X9KTWSVchQ8MK1c=",
+        "lastModified": 1784291704,
+        "narHash": "sha256-GOVjf8+dqf7bU3E+LvKhqRFrMaptNtLIXkncGCIrj3A=",
         "ref": "refs/heads/master",
-        "rev": "f3ab054aef8cce1fc2b56fec48a20e1764e017a1",
-        "revCount": 9,
+        "rev": "fbe2ae6f3241f4b289590cd64fea5a935aeca85d",
+        "revCount": 10,
         "type": "git",
         "url": "git://git.mathematicaster.org/www/assets.git"
       },
diff --git a/flake.nix b/flake.nix
index b826f76..cfba594 100644
--- a/flake.nix
+++ b/flake.nix
@@ -85,7 +85,7 @@
           # site = config.packages.www-main;
           site = pkgs.haskellPackages.www-main;
           texPath = [
-            pkgs.texlive.combined.scheme-full
+            pkgs.texliveFull
           ];
         };
         site = pkgs.runCommandLocal "build-site" {} ''
-- 
cgit v1.3.1